Law of Exponents: Product Rules

Front

What is the Product Rule of Exponents?

Back

When multiplying two expressions with the same base, add the exponents. For example, a^m * a^n = a^(m+n).

Front

Simplify: (-4r^5)(2r^8)

Back

-8r^13

Front

Simplify: 3x^4 ⋅ 6x^6

Back

18x^10

Front

Simplify: r^6 ⋅ r^2 ⋅ r^3

Back

r^11

Front

Simplify: (x^2)(x^5)

Back

x^7

Front

Simplify: 2x^2y^5z(4x^3y^2z)

Back

8x^5y^7z^2

Front

What happens to the exponents when multiplying terms with the same base?

Back

The exponents are added together.

Front

If a^3 * a^2 = a^x, what is the value of x?

Back

x = 5.

Front

What is the result of 5^2 * 5^3?

Back

5^5 or 3125.

Front

How do you simplify expressions with different bases?

Back

You cannot combine them using the Product Rule; simplify each base separately.